We study the exotic decay of the 125 GeV Higgs boson (h) into a pair of light spin-0 particles (\(\phi \)) which subsequently decay and result in a 4b final state. This channel is well motivated in models with an extended Higgs sector. Instead of searching at the Large Hadron Collider (LHC) and the high luminosity LHC (HL-LHC) which are beset by large standard model (SM) backgrounds, we investigate this decay channel at the much cleaner Large Hadron Electron Collider (LHeC). With some simple selection cuts this channel becomes nearly free of background at this ep machine, in sharp contrast to the situation at the (HL-)LHC. With a parton level analysis we show that for the \(\phi \) mass range \([20,60]~{\text{ GeV }}\), with \(100~{\text{ fb }^{-1}}\) luminosity the LHeC is generally capable of constraining \(C_{4b}^2\equiv \kappa _{V}^2\times {\mathrm {Br}}(h\rightarrow \phi \phi )\times {\mathrm {Br}}^2(\phi \rightarrow b\bar{b})\) (\(\kappa _{V}\) denotes the \(hVV(V=W,Z)\) coupling strength relative to the SM value) to a few percent level (\(95\%\) CLs). With \(1~{\text{ ab }^{-1}}\) luminosity \(C_{4b}^2\) at a few per mille level can be probed. These sensitivities are much better than the HL-LHC performance and demonstrate the important role expected to be played by the LHeC in probing exotic Higgs decay processes, in addition to the already proposed invisible Higgs decay channel.

Eur. Phys. J. C
Exotic Higgs decay h → φφ → 4b at the LHeC
Shang Liu 2
Yi-Lei Tang 1
Chen Zhang 2
Shou-hua Zhu 0 1 2
0 Collaborative Innovation Center of Quantum Matter , Beijing 100871 , China
1 Center for High Energy Physics, Peking University , Beijing 100871 , China
2 Institute of Theoretical Physics and State Key Laboratory of Nuclear Physics and Technology, Peking University , Beijing 100871 , China
We study the exotic decay of the 125 GeV Higgs boson (h) into a pair of light spin-0 particles (φ) which subsequently decay and result in a 4b final state. This channel is well motivated in models with an extended Higgs sector. Instead of searching at the Large Hadron Collider (LHC) and the high luminosity LHC (HL-LHC) which are beset by large standard model (SM) backgrounds, we investigate this decay channel at the much cleaner Large Hadron Electron Collider (LHeC). With some simple selection cuts this channel becomes nearly free of background at this ep machine, in sharp contrast to the situation at the (HL-)LHC. With a parton level analysis we show that for the φ mass range [20, 60] GeV, with 100 fb−1 luminosity the LHeC is generally capable of constraining C42b ≡ κV2 × Br(h → φφ) × Br2(φ → bb¯) (κV denotes the hV V (V = W, Z ) coupling strength relative to the SM value) to a few percent level (95% CLs). With 1 ab−1 luminosity C42b at a few per mille level can be probed. These sensitivities are much better than the HL-LHC performance and demonstrate the important role expected to be played by the LHeC in probing exotic Higgs decay processes, in addition to the already proposed invisible Higgs decay channel.
1 Introduction
The discovery of the 125 GeV Higgs boson (denoted h) [
1,2
]
not only deepens our understanding of the mechanism of
electroweak symmetry breaking but also opens new avenues
for searching for physics beyond the Standard Model (SM)
which is required to clarify the unexplained theoretical and
observational issues such as the problem of naturalness, the
existence of dark matter and the observed baryon asymmetry
of the universe. One of such avenues is exotic Higgs decay,1
which is only loosely constrained by Higgs signal strength
measurements. The combination of ATLAS and CMS Run I
results constrains undetected Higgs decay branching ratio to
be smaller than about 34% at 95% C.L. assuming κV ≤ 1 [4]
(κV denotes hV V (V = W, Z ) coupling strength relative
to SM assuming κV ≡ κW = κZ ). The ultimate
sensitivity on undetected Higgs decay branching ratio via indirect
measurements at the High Luminosity Large Hadron
Collider (HL-LHC) is estimated to be O (5–10%) [
5
]. On the
other hand, due to the expected extremely narrow width of
the Higgs boson, even a rather weak coupling between it and
any new light degrees of freedom can naturally induce a
sizable exotic decay branching fraction. One such possibility
is h → φφ, where φ denotes a light spin-0 particle, with
mass less than about 62.5 GeV so that this decay channel
is kinematically allowed. φ can be CP-even or CP-odd, or
even a CP-mixed state. If its mass is greater than 2mb, then
in most models which approximately obey Yukawa ordering
φ will mainly decay to bb¯. This decay channel is well
motivated in a wide class of Beyond the Standard Model (BSM)
theories [
5
], such as the Next to Minimal Supersymmetric
Standard Model (NMSSM), Higgs singlet extension of the
SM, general extended Higgs sector models [
6
], and little
Higgs models. Quite a few phenomenology studies already
exist with respect to this channel at the LHC [
7–11
], with or
without using jet substructure techniques. Due to large QCD
backgrounds in gluon fusion and vector boson fusion
channels, the LHC searches generally focus on the VH associated
production channel. However, this channel suffers from large
top quark backgrounds. A recent ATLAS analysis [
12
] using
3.2 fb−1 13 TeV data made the first attempt to constrain this
channel using WH associated production but the sensitivity
1 In this paper we study exotic decays of the 125 GeV Higgs boson. For
exotic decays of additional Higgs bosons we refer the interested reader
to a recent study [
3
].
is currently quite weak (even Br(h → φφ → 4b) = 100%
cannot be constrained assuming κV = 1).
The not-so-clean hadron–hadron collision environment
motivates us to consider better places to search for this
exotic Higgs decay channel. Here we consider using the
Large Hadron Electron Collider (LHeC) [
13
] to explore
h → φφ → 4b. The LHeC is a proposed lepton–hadron
collider which is designed to collide a 60 GeV electron beam
with the 7 TeV proton beam of the HL-LHC. It is supposed
to run synchronously with the HL-LHC and may deliver an
integrated luminosity as high as 1000 fb−1 [
14
]. The
electron beam may have −0.9 polarization [
14
]. It is worth
noticing that with such high collision energy and luminosity, the
LHeC indeed becomes a Higgs boson factory [
14
]. With
Higgs boson production cross section of about 200 fb−1,
the LHeC will provide amazing opportunities for precision
Higgs physics, due to the fact that major QCD backgrounds
will be much smaller than LHC and the complication due to
pile-up will be greatly reduced. Previous studies on Higgs
physics at the LHeC include measuring bottom Yukawa
coupling [
13,15,16
], anomalous gauge–Higgs coupling [
17–19
],
invisible Higgs decay [
20
] and MSSM Higgs production [
21
].
Studies on charm Yukawa measurements has been reported
in [
22
]. The impact of double Higgs production at the higher
energy ep collider FCC-he on Higgs-self coupling
measurement has also been studied [
23,24
].
To quantitatively estimate the sensitivity of the LHeC to
the exotic Higgs decay h → φφ → 4b, we perform a parton
level study for the signal and background in the next
section. The signal definition depends on the required number
of b-tagged jets. Here for simplicity and a clear identification
of signal we require tagging at least four b-tagged jets. We
provide the expected LHeC sensitivity for φ mass between
15 and 60 GeV and investigate the robustness of our results
under variation of b-tagging performance and
pseudorapidity coverage. We also translate our results into the expected
exclusion power in the parameter space of the Higgs
singlet extension of the SM. In the last section we present our
discussion and conclusion.
2 Collider sensitivity
The exotic Higgs decay h → φφ → 4b can be simply
characterized by the following effective interaction Lagrangian
for a new real scalar degree of freedom φ:
Le f f = λh vhφ2 + λbφb¯b + Lφ decay,other
(1)
In the above v = 246 GeV. λh and λb are real dimensionless
parameters and Lφ decay,other denotes the part of Lagrangian
which mediates the decay of φ into final states other than
bb¯. The part of Lagrangian Le f f − Lφ decay,other has been
W −
taken as CP-even without loss of generality. New physics
may also modify hV V (V = W, Z ) coupling which affects
the Higgs production rate and kinematics. We assume the
hV V (V = W, Z ) coupling is purely CP-even. Assuming
narrow width approximation is valid for both h and φ, we
can express the collider reach for h → φφ → 4b via the
following quantity:
C42b = κV × Br(h → φφ) × Br2(φ → bb¯)
2
(2)
for a given value of the φ mass mφ .
There are two major Higgs production channels at the
LHeC: charged current (CC) and neutral current (NC). Due
to the accidentally suppressed electron NC coupling, NC
Higgs cross section is much less than that of CC [
16
].
Therefore in the following we only focus on CC process, although
in a more detailed analysis the NC process should also be
included to enhance the overall statistical significance.
The signal process of CC Higgs production is
eq → νehq
→ νeφφq
→ νebb¯bb¯q
(3)
The corresponding Feynman diagram is shown in Fig. 1. The
signal signature thus contains at least five jets (in which at
least four jets are b-tagged) plus missing transverse energy.
The backgrounds can be classified into charged current
(CC) deeply inelastic scattering (DIS) backgrounds and
photoproduction (PHP) backgrounds. From a parton level point
of view, CC DIS backgrounds all have genuine E/ T in the
final state which comes from neutrinos produced in the hard
scattering or decay of heavy resonances (W, Z , t, h). When
it comes to PHP backgrounds, only PHP production of heavy
resonances (W, Z , t, h) could produce such genuine E/ T .
However, these PHP processes (which involve the on-shell
production of heavy resonances (W, Z , t, h)) are found to
be negligible in the total background. On the other hand,
PHP multijet production (including heavy flavor jets) could
produce E/ T only via energy mismeasurement and neutrinos
from hadron decay, which means that it could be suppressed
efficiently through a sufficiently large requirement of E/ T .
¯
b
¯
b
¯
b
q
e−
¯
b
b
e−
γ
g
νe
W
νe
b
b
W
¯
t
g
¯
b
¯
b
b
q¯
q
¯
c
s
b
The CC backgrounds can be further classified according to
the number of heavy resonances (W, Z , t, h) produced which
further decay to result in a large number of b-tagged jets. We
found that if in one process the number of heavy resonances
involved is greater than or equal to two, then its
contribution to the total background is always negligible. Therefore
in the following we only consider the following CC
backgrounds: CC multijet, CC W +jets, CC Z +jets, CC t +jets,
CC h+jets. Here “multijet” and “jets” contain jets of all
flavor (g, u, d, s, c, b). Higgs decay to 4b via SM processes is
also included as a background, in CC h+ jets. Figure 2
displays representative Feynman diagrams for these background
processes.
To simulate the signal and backgrounds, we implement
the effective interaction in Eq. (1) into FeynRules [
25
]. The
generated model file together with the SM is then imported
by MadGraph5_aMC@NLO [
26
]. The Higgs boson mass
is taken to be mh = 125 GeV. The φ mass is scanned in
the region [
15, 60
] GeV with 1 GeV step size. The collider
parameter is taken to be Ee = 60 GeV, E p = 7 TeV with
electron beam being −0.9 polarized. The signal and
background samples are generated by MadGraph5_aMC@NLO
at leading order with NNPDF2.3 LO PDF [
27
] and the
renormalization and factorization scale is set dynamically by
MadGraph default. The NLO QCD correction to the signal
process are known to be small [
28
]. In the following we take
all the signal and background K-factors to be 1 although
we expect the correct background normalization could be
obtained from data. We apply jet energy smearing according
to the following energy resolution formula:
σEE = √αE ⊕ β (4)
where α = 0.45 GeV1/2, β = 0.03 [
13
]. We consider the
following four scenarios of b-tagging performance for jets with
pT > 20 GeV ( b denotes the efficiency of b-jet, while c and
g,u,d,s denote the faking probability of c-jet and g, u, d,
sjet, respectively):
(A) b = 70%, c = 10%, g,u,d,s = 1%;
(B) b = 70%, c = 20%, g,u,d,s = 1%;
(C) b = 60%, c = 10%, g,u,d,s = 1%;
(D) b = 60%, c = 20%, g,u,d,s = 1%.
The LHeC detector (including the tracker) is expected to
have a very large pseudorapidity coverage [
29
] and therefore
we assume the b-tagging performance listed above is valid up
to |η| < 5. We will also show the expected sensitivities with
smaller b-tagging pseudorapidity coverage |η| < 4 and |η| <
3, which turn out to change only slightly compared to the
|η| < 5 case. Event analysis is performed by MadAnalysis
5 [
30
].
The event selection in the 4b-tagging case first requires at
least five jets satisfying the following basic cuts:
pT j > 20 GeV, |η j | < 5.0,
R j j > 0.4
(5)
Events with additional charged leptons are vetoed. To
suppress the photoproduction background, we exclude events
which can be tagged by an electron tagger and also require
The four b-tagged jets which have the closest invariant mass
to mh are required to have their invariant mass m4b lie in the
following mass window:
E/ T > E0
(6)
|m4b − mh | < 20 GeV
Here E0 denotes the threshold of transverse missing energy.
In the following we take E0 = 40 GeV as the default choice
and assume PHP backgrounds can be accordingly suppressed
to a negligible level compared to the total background. This
rough estimate of the missing energy threshold is inspired
by a naive simulation of direct photoproduction j + 4b
process.2 A thorough and detailed detector simulation of multijet
photoproduction would be needed to determine the best E0
(perhaps in synergy with appropriate missing energy
isolation cuts or a cut on the ratio Vap/ Vp of transverse energy
flow anti-parallel and parallel to the hadronic final state
transverse momentum vector [
32
]), which is, however, beyond the
scope of the present paper. In the cut flow tables below we
will also show the signal and total background in the case
that E0 needs to be increased to 60 GeV.
Then we impose the 4b-tagging requirement:
At least four b-tagged jets in |η| < 5.0
(7)
2 According to previous experience [
31
], in PHP multijet processes
the resolved component becomes smaller than the direct component
when a hard scale is involved. Therefore as in [
16
], we do not expect
resolved photoproduction j + 4b to be a leading component in PHP
backgrounds. For direct photoproduction j +4b (photon virtuality Q2 <
1 GeV2), we find a cross section of about 0.9 fb after basic cuts and
4b-tagging requirement, with electron tagging and 4b and 2b invariant
mass requirement a cross section reduction by two orders of magnitude
could be expected. Because the total CC backgrounds are at 10−3 fb to a
few times 10−4 fb level depending on mφ , the PHP backgrounds would
become negligible if the E/ T > E0 cut and perhaps missing energy
isolation cuts could bring down the PHP cross section by another two
or three orders of magnitude, which could be achieved for E0 ∼ 40 −
60 GeV by our current rough estimation, given the situation that the
LHeC detector is supposed to have better resolution and coverage than
LHC.
Finally we utilize the event structure of the signal: for the
four b-tagged jets picked out in the previous step, we group
them into two pairs such that the absolute value of the
invariant mass difference between these two pairs is smallest
among all grouping possibilities. Then we require the
invariant masses of these b-jet pairs both lie in the following mass
window:
|m2b,i − mφ | < 10 GeV, i = 1, 2
Here m2b,i , i = 1, 2 denote the invariant mass of the two
“correctly” grouped b-jet pairs, respectively.
We present cut flow tables (Tables 1, 2, 3) for three
benchmark masses mφ = 20, 40, 60 GeV under b-tagging
performance scenario (A). Only CC backgrounds are listed
because PHP backgrounds are expected to be negligible
due to electron tagging and an appropriate missing energy
requirement. For the decay of t , W, Z in backgrounds, the
following two cases are both considered and included in our
results. One is the decay to a minimal number of partons, i.e.
t → bqq, W → qq, Z → qq, with each parton identified
as one jet. The other case is that one additional bb¯ pair is
radiated from the decay products of t , W, Z . For t +jets the
second kind of process is found to contribute sizably to the
total background. For the h+jets background, only h → bb
and h → 4b via tree-level SM processes are considered. Due
to limited Monte Carlo statistics, there are slight differences
among the three tables for the first four cuts on backgrounds.
The cross section numbers shown in the tables correspond
to the default choice E0 = 40 GeV, except that in the last
row of each table for the signal and total background we
show in parentheses the final cross sections corresponding
to E0 = 60 GeV. From the tables it can be concluded that
Table 2 The cross section (in unit of fb) of the signal and major
backgrounds after application of each cut in the corresponding row. Lepton
veto and electron anti-tagging is implicit in basic cuts. Signal
corresponds to C42b = 1, mφ = 40 GeV. Here we assume b-tagging
perforTable 3 The cross section (in unit of fb) of the signal and major
backgrounds after application of each cut in the corresponding row. Lepton
veto and electron anti-tagging is implicit in basic cuts. Signal
corresponds to C42b = 1, mφ = 60 GeV. Here we assume b-tagging
perforthe h → φφ → 4b channel at the LHeC is almost
background free—with 100 fb−1 luminosity the expected number
of background events is at most O(0.1), while the remaining
signal cross section is O(1 fb) for C42b = 1. This is in sharp
contrast to the situation at the (HL-)LHC where the signal is
buried in large top quark backgrounds.
Figure 3 shows the expected 95% CLs [
33, 34
] exclusion
limits and 5σ discovery reach at the LHeC for the C42b
quandifferent b-tagging scenarios (A)(B)(C)(D) (see the text and legend).
E0 = 40 GeV is assumed
tity in the mass range [15, 60] GeV assuming 100 fb−1 and
1 ab−1 luminosity. Various b-tagging performance scenarios
are considered in the plots, all assuming a b-tagging
pseudorapidity coverage |η| < 5. Because the expected number of
background events is quite small, in setting exclusion limits
and discovery reach we use exact formulas of the Poisson
distribution for a discrete random variable. This leads to some
small discontinuities at certain mφ values when the expected
tions are considered. The plots indicate that the sensitivity
reach of the LHeC for this channel is not very sensitive to
b-tagging pseudorapidity coverage.
3 Constraints on the Higgs singlet extension of the SM
We now consider the interpretation of the expected sensitivity
of the LHeC in the context of Higgs singlet extension of the
SM. For simplicity we consider the Higgs singlet extension
studied in [
35
]. In this model, an additional real singlet scalar
S is added to the SM. The Lagrangian of the Higgs kinetic
and potential terms is extended to the following form:
Ls = (Dμ )† Dμ
+ ∂μ S∂μ S − V ( , S)
with scalar potential
V ( , S) = −m2 †
h √+2 x .
Here v = 246 GeV ensures the correct mass generation for
W, Z bosons and SM fermions. The gauge eigenstates h˜, h
can be related to mass eigenstates φ, h via an orthogonal
rotation
limits/reach are interpreted as the limits/reach for the median
of background-only or signal plus background hypothesis, as
can be seen from the plots.
From Fig. 3 it can easily be seen that for mφ in the
[
20, 60
] GeV range the LHeC with 100 fb−1 luminosity is
capable of probing C42b to a few percent level while with
1 ab−1 luminosity the LHeC will eventually probe C42b down
to a few per mille level, both at 95% CLs. We note that for
mφ = 20, 40, 60 GeV, the 95% CLs upper limit on C42b is
about 0.3%(0.5%), 0.2%(0.4%), 0.1%(0.2%) respectively,
for b-tagging scenario (A), assuming E0 = 40 GeV(60 GeV).
The result is generally insensitive to mistag rates of c-jets,
because with the requirement of at least four b-tagged jets,
fake backgrounds do not contribute much to the total
background. On the other hand the final signal rate is
approximately proportional to the fourth power of the b-tagging
efficiency, thus it will be relatively important to maintain a
high b-tagging efficiency to retain more signal events. As can
be expected, the sensitivity drops quickly when mφ becomes
smaller than about 20 GeV due to the collimation of φ decay
products that renders the resolved analysis inefficient. A jet
substructure analysis is needed to improve the sensitivity in
this mass region, which we leave for future study. On the
other hand the sensitivity improves as mφ increases from
about 40–60 GeV. This is mainly because the b-jets from
h → φφ → 4b decay in the mφ = 60 GeV case are more
likely to pass the basic cuts (especially, the pT j > 20 GeV
cut) compared to the mφ = 40 GeV case.
Figure 4 also shows the expected 95% CLs exclusion
limits and 5σ discovery reach at the LHeC for the C42b quantity in
the mass range [
15, 60
] GeV assuming 100 fb−1 and 1 ab−1
luminosity. Here b-tagging performance is fixed to scenario
(A) but various b-tagging pseudorapidity coverage
condisponds to different b-tagging pseudorapidity coverage (see the legend).
E0 = 40 GeV is assumed
(10)
(11)
(12)
point is colored according to its C42b value for reference. Also shown are
current LEP and LHC bounds, and expected future HL-LHC bounds.
See text for detail
φ
h =
cos α − sin α
sin α cos α
h
h˜ .
Now it is convenient to parameterize the model in terms of
five more physical quantities: (mφ , mh are masses of φ and
h respectively)
v
mφ , mh , α, v, tan β ≡ x .
The translation formulas between these quantities and
original parameters in the Lagrangian can be found in [
35
]. We
are interested in the case in which the additional Higgs boson
is lighter, therefore we fix mh = 125 GeV and allow three
parameters mφ , α, tan β to vary. Here we focus on the more
interesting region where sin α → −1 which also allows
for a special direction tan β = − cot α, which results in
a vanishing Br(h → φφ) [
35
]. We consider three
benchmark values of [
4
] mφ (mφ = 20, 40, 60 GeV) and plot
the current LEP and LHC constraints and future HL-LHC
and LHeC constraints on the tan β − sin α plane; see Fig. 5.
Each point is colored according to its C42b value for
reference. The factor Br2(φ → bb¯) appeared in C42b definition
(13)
(14)
Eq. (2) is almost at a constant value 0.77 in the mass range
mφ ∈ [
20, 60
] GeV [
36
]. The deep black regions which
corresponds to very small C42b values slightly tilt upwards
with the decreasing of | sin α| from about 0.995 to 0.980.
In this range these regions just center around the
abovementioned special direction tan β = − cot α, which makes
Br(h → φφ) vanish [
35
] and renders its vicinity difficult
to probe through exotic Higgs decay search. The LEP
constraints (green dashed line) come from direct search for
additional Higgs bosons and is taken directly from [
35
]. Points
on the right side of the green dashed line is excluded at 95%
confidence level. This indicates that LEP search forces the
mixing between two Higgses to be very small for the
scenario in which there is a light Higgs boson in the mass range
(mφ ∈ [
20, 60
] GeV). In such a case there cannot be
sizable deviation of Higgs signal strength due to Higgs
mixing. However, the opening of exotic Higgs decay h → φφ
could lead to sizable suppression of 125 GeV Higgs
signal strengths. The LHC Run I constraints (white solid line)
come from the 125 GeV Higgs signal strength
measurements [
4
]. The regions between the two white solid lines
for mφ = 20, 40 GeV (and the region below the white solid
lines for mφ = 60 GeV case) are allowed by LHC Run I
measurements at 2σ level. We translated the HL-LHC projection
of the precision of Higgs signal strength measurements [
37
]
into constraints (yellow solid line “HL-LHC ind.”) on the
parameter space of the Higgs singlet extension of the SM
(assuming half theoretical uncertainties, according to [
37
]).
At the (HL-)LHC, h → φφ → 4b can be directly probed via
W h associated production, as has been done by ATLAS [
12
].
However, current constraint from this method is quite weak
and even C42b = 1 cannot be bound. We extrapolate the
current constraint [
12
] to 3 ab−1 HL-LHC, with a very optimistic
assumption that all selection efficiency can be maintained and
all systematic uncertainties scale with the square root of
luminosity. The corresponding 95% CLs exclusion limits is
plotted as yellow dotted line “HL-LHC dir.(opt.)”. It can be seen
that even with this very optimistic assumption the sensitivity
of the direct search from W h channel is at most comparable
to the indirect constraint from the HL-LHC 125 GeV Higgs
signal strength measurements. The LHeC 1 ab−1 95% CLs
sensitivity is plotted as the red solid lines, assuming b-tagging
scenario (A), b-tagging pseudorapidity coverage |η| < 5.0
and E0 = 40 GeV. The LHeC is expected to exclude region
outside the red solid lines if no new physics exists. It is
obvious that the LHeC exclusion capability extends to the deep
black region which represents very small C42b values. If no
lepton colliders are available before the end of the HL-LHC,
much of the parameter space of the Higgs singlet extension
model could only be reached via the ep machine.
4 Discussion and conclusion
In this paper we studied the LHeC sensitivity to the exotic
Higgs decay process h → φφ → 4b in which φ denotes a
spin-0 particle lighter than half of 125 GeV. We performed a
parton level analysis and showed that with 1 ab−1 luminosity
the LHeC is able to exclude C42b at a fer per mille level (95%
CLs), when only statistical uncertainties are included. To
maintain the sensitivity, it is important to choose a b-tagging
working point with relatively large b-tagging efficiency. The
sensitivity is not very sensitive to the variation of b-tagging
pseudorapidity coverage from 3 to 5. Using the Higgs
singlet extension of the SM as an illustration, we showed that
the LHeC direct search of h → φφ → 4b is the most
sensitive probe of much of the parameter space of the model
in the future, if no lepton colliders are available. Of course
this LHeC search will also deliver significant impacts on the
scalar sector of other BSM theories when one of the scalar
boson lies in the mass range ∼(2mb, mh /2).
The analysis presented here can be further improved in
several aspects. First is of course a more realistic
estimation of the signal and backgrounds including parton shower
and more detailed detector effects. Especially for multijet
final states a parton shower correctly merged to matrix
element will be highly desirable. Secondly, we could further
utilize the sample with the requirement of less b-tagged jets
or even less reconstructed jets, e.g. three b-tagged jets. This
technique has already been used in [
12
] and is expected to
further improve the sensitivity, especially in the first stages
of data collection when statistics is small. Thirdly, we have
only applied a cut-based analysis with very simple variables.
A further multivariate analysis may deliver additional gain in
sensitivity. Furthermore, the sensitivity in the mφ < 20 GeV
mass range could be improved via a jet substructure analysis,
as has been emphasized. Besides these directions of
exploration, it should, however, be emphasized that in the current
analysis PHP backgrounds are assumed to be negligible
compared to CC backgrounds under the condition discussed in
Sect. 2. A more detailed detector simulation is thus needed
to pin down the event selection conditions required to
suppress PHP backgrounds. We also note that in the present
study systematic uncertainties have not been included.
However, since the expected background event number is very
small, we expect that the obtained sensitivity (discovery and
exclusion reach) would be qualitatively stable against
systematic uncertainties, which means that the 1 ab−1 LHeC
could still do much better than the HL-LHC with respect to
the h → φφ → 4b search.
The exotic Higgs decays constitute an intriguing and
important part of Higgs physics which deserve
comprehensive theoretical and experimental investigations.
Previous attempts and attention have nearly all been devoted to
hadron–hadron collisions or e+e− collisions. We
demonstrate in this paper that for certain important processes which
suffer from large backgrounds in hadron–hadron collisions,
it is clearly superior to conduct the search at a concurrent ep
collider, if an e+e− machine with sufficient center-of-mass
energy is not available. In that case, it is highly expected
that the ep machine will play an important role in precision
Higgs studies, including the study of exotic Higgs decays
like h → E/ T [
20
], h → φφ → 4b and other channels beset
by jets or E/ T [
38,39
].
Acknowledgements We would like to thank Qing-Hong Cao, Manuel
Drees, Uta Klein, Masahiro Kuze, Yan-Dong Liu, Ying-Nan Mao,
Masahiro Tanaka and Hao Zhang for helpful discussions. This work was
supported in part by the Natural Science Foundation of China (Grants
No. 11135003, No. 11375014 and No. 11635001) and by the China
Postdoctoral Science Foundation under Grant No. 2016M600006.
Open Access This article is distributed under the terms of the Creative
Commons Attribution 4.0 International License (http://creativecomm
ons.org/licenses/by/4.0/), which permits unrestricted use, distribution,
and reproduction in any medium, provided you give appropriate credit
to the original author(s) and the source, provide a link to the Creative
Commons license, and indicate if changes were made.
Funded by SCOAP3.
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